{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "# Ignore numpy dtype warnings. These warnings are caused by an interaction\n",
    "# between numpy and Cython and can be safely ignored.\n",
    "# Reference: https://stackoverflow.com/a/40846742\n",
    "warnings.filterwarnings(\"ignore\", message=\"numpy.dtype size changed\")\n",
    "warnings.filterwarnings(\"ignore\", message=\"numpy.ufunc size changed\")\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "%matplotlib inline\n",
    "import ipywidgets as widgets\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual\n",
    "import nbinteract as nbi\n",
    "\n",
    "sns.set()\n",
    "sns.set_context('talk')\n",
    "np.set_printoptions(threshold=20, precision=2, suppress=True)\n",
    "pd.options.display.max_rows = 7\n",
    "pd.options.display.max_columns = 8\n",
    "pd.set_option('precision', 2)\n",
    "# This option stops scientific notation for pandas\n",
    "# pd.set_option('display.float_format', '{:.2f}'.format)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "def df_interact(df, nrows=7, ncols=7):\n",
    "    '''\n",
    "    Outputs sliders that show rows and columns of df\n",
    "    '''\n",
    "    def peek(row=0, col=0):\n",
    "        return df.iloc[row:row + nrows, col:col + ncols]\n",
    "    if len(df.columns) <= ncols:\n",
    "        interact(peek, row=(0, len(df) - nrows, nrows), col=fixed(0))\n",
    "    else:\n",
    "        interact(peek,\n",
    "                 row=(0, len(df) - nrows, nrows),\n",
    "                 col=(0, len(df.columns) - ncols))\n",
    "    print('({} rows, {} columns) total'.format(df.shape[0], df.shape[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {
    "scrolled": true,
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "df = pd.read_csv('water_large.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "from collections import namedtuple\n",
    "Curve = namedtuple('Curve', ['xs', 'ys'])\n",
    "\n",
    "def flatten(seq): return [item for subseq in seq for item in subseq]\n",
    "\n",
    "def make_curve(clf, x_start=-50, x_end=50):\n",
    "    xs = np.linspace(x_start, x_end, num=100)\n",
    "    ys = clf.predict(xs.reshape(-1, 1))\n",
    "    return Curve(xs, ys)\n",
    "\n",
    "def plot_data(df=df, ax=plt, **kwargs):\n",
    "    ax.scatter(df.iloc[:, 0], df.iloc[:, 1], s=50, **kwargs)\n",
    "\n",
    "def plot_curve(curve, ax=plt, **kwargs):\n",
    "    ax.plot(curve.xs, curve.ys, **kwargs)\n",
    "    \n",
    "def plot_curves(curves, cols=2):\n",
    "    rows = int(np.ceil(len(curves) / cols))\n",
    "    fig, axes = plt.subplots(rows, cols, figsize=(10, 8),\n",
    "                             sharex=True, sharey=True)\n",
    "    for ax, curve, deg in zip(flatten(axes), curves, degrees):\n",
    "        plot_data(ax=ax, label='Training data')\n",
    "        plot_curve(curve, ax=ax, label=f'Deg {deg} poly')\n",
    "        ax.set_ylim(-5e10, 170e10)\n",
    "        ax.legend()\n",
    "        \n",
    "    # add a big axes, hide frame\n",
    "    fig.add_subplot(111, frameon=False)\n",
    "    # hide tick and tick label of the big axes\n",
    "    plt.tick_params(labelcolor='none', top='off', bottom='off',\n",
    "                    left='off', right='off')\n",
    "    plt.grid(False)\n",
    "    plt.title('Polynomial Regression')\n",
    "    plt.xlabel('Water Level Change (m)')\n",
    "    plt.ylabel('Water Flow (Liters)')\n",
    "    plt.tight_layout()\n",
    "    \n",
    "def print_coef(clf):\n",
    "    reg = clf.named_steps['reg']\n",
    "    print(reg.intercept_)\n",
    "    print(reg.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "X = df.iloc[:, [0]].as_matrix()\n",
    "y = df.iloc[:, 1].as_matrix()\n",
    "\n",
    "degrees = [1, 2, 8, 12]\n",
    "clfs = [Pipeline([('poly', PolynomialFeatures(degree=deg, include_bias=False)),\n",
    "                  ('reg', LinearRegression())])\n",
    "        .fit(X, y)\n",
    "        for deg in degrees]\n",
    "\n",
    "curves = [make_curve(clf) for clf in clfs]\n",
    "\n",
    "ridge_clfs = [Pipeline([('poly', PolynomialFeatures(degree=deg, include_bias=False)),\n",
    "                        ('reg', Ridge(alpha=0.1, normalize=True))])\n",
    "        .fit(X, y)\n",
    "        for deg in degrees]\n",
    "\n",
    "ridge_curves = [make_curve(clf) for clf in ridge_clfs]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regularization Intuition\n",
    "\n",
    "We begin our discussion of regularization with an example that illustrates the importance of regularization.\n",
    "\n",
    "## Dam Data\n",
    "\n",
    "The following dataset records the amount of water that flows out of a large dam on a particular day in liters and the amount the water level changed on that day in meters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "scrolled": true,
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>water_level_change</th>\n",
       "      <th>water_flow</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-15.936758</td>\n",
       "      <td>6.042233e+10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-29.152979</td>\n",
       "      <td>3.321490e+10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>36.189549</td>\n",
       "      <td>9.727064e+11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>7.085480</td>\n",
       "      <td>2.363520e+11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>46.282369</td>\n",
       "      <td>1.494256e+12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>14.612289</td>\n",
       "      <td>3.781463e+11</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>23 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    water_level_change    water_flow\n",
       "0           -15.936758  6.042233e+10\n",
       "1           -29.152979  3.321490e+10\n",
       "2            36.189549  9.727064e+11\n",
       "..                 ...           ...\n",
       "20            7.085480  2.363520e+11\n",
       "21           46.282369  1.494256e+12\n",
       "22           14.612289  3.781463e+11\n",
       "\n",
       "[23 rows x 2 columns]"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting this data shows an upward trend in water flow as the water level becomes more positive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1785ac50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot.scatter(0, 1, s=50);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To model this pattern, we may use a least squares linear regression model. We show the data and the model's predictions on the plot below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1769ecf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot.scatter(0, 1, s=50);\n",
    "plot_curve(curves[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The visualization shows that this model does not capture the pattern in the data—the model has high bias. As we have previously done, we can attempt to address this issue by adding polynomial features to the data. We add polynomial features of degrees 2, 8, and 12; the chart below shows the training data with each model's predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1789d828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_curves(curves)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, the degree 12 polynomial matches the training data well but also seems to fit spurious patterns in the data caused by noise. This provides yet another illustration of the bias-variance tradeoff: the linear model has high bias and low variance while the degree 12 polynomial has low bias but high variance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Examining Coefficients\n",
    "\n",
    "Examining the coefficients of the degree 12 polynomial model reveals that this model makes predictions according to the following formula:\n",
    "\n",
    "$$\n",
    "207097470825 + 1.8x + 482.6x^2 + 601.5x^3 + 872.8x^4 + 150486.6x^5 \\\\\n",
    "    + 2156.7x^6 - 307.2x^7 - 4.6x^8 + 0.2x^9 + 0.003x^{10} - 0.00005x^{11} + 0x^{12}\n",
    "$$\n",
    "\n",
    "where $ x $ is the water level change on that day.\n",
    "\n",
    "The coefficients for the model are quite large, especially for the higher degree terms which contribute significantly to the model's variance ($ x^5 $ and $ x^6 $, for example)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Penalizing Parameters\n",
    "\n",
    "Recall that our linear model makes predictions according to the following, where $ \\theta $ is the model weights and $ x $ is the vector of features:\n",
    "\n",
    "$$\n",
    "f_\\hat{\\theta}(x) = \\hat{\\theta} \\cdot x\n",
    "$$\n",
    "\n",
    "To fit our model, we minimize the mean squared error cost function, where $ X $ is used to represent the data matrix and $ y $ the observed outcomes:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "L(\\hat{\\theta}, X, y)\n",
    "&= \\frac{1}{n} \\sum_{i}(y_i - f_\\hat{\\theta} (X_i))^2\\\\\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "To minimize the cost above, we adjust $ \\hat{\\theta} $ until we find the best combination of weights regardless of how large the weights are themselves. However, we have found that larger weights for more complex features result in high model variance. If we could instead alter the cost function to penalize large weight values, the resulting model will have lower variance. We use regularization to add this penalty."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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